Induction heater



March 26, 1935. T. H. LONG INDUCTION HEATER Filed May 20, 1950 lNvENToR730/7745 of/j.

ATTRNEY Patented Mar. 26, 1935 UNITED sTATEs INDUCTION HEATER Thomas H.Long, Iwin, Pa., assignor to Westinghouse Electric & ManufacturingCompany, a corporation of Pennsylvania Application May 20, 1930, SerialNo. 453,908

My invention relates to improvements in heating apparatus and it hasparticular relation to inductive-heating equipment.

In inductive heating apparatus, constructed and operated according tothe teachings 0f the prior art, it has been customary to use a high.-frequency motor-generator set and to correct for low power factor bydisposing a plurality of static condensers in series4 or in parallelwith-the generator supplying the exciting currentl to the inducingcoils. This methodof operating has proved rather expensive, by reason ofthe cost of the condensers and generator set involved.

On the other hand, it is possible toselect the dimensions of theinducing coil and the frequency of the inducing field, in such manner asto give these properties of the equipment values so related to thecharacteristics of the charge that a maximum, or a considerablyimproved, power factor is obtained at relatively low frequencies orstandard frequencies such as cycles. Inductiveheating equipment havingthe requisite tractability in its `properties has a wide range ofusefulness.

It is, accordingly, an object of my invention to provideinductive-heating apparatus the properties of which are so inter-relatedthat the ratio of the irreversible energy induced in a hypotheticalcharge, having the properties of conductors most commonly treated in theapparatus, to the reversible energy induced in the charge issubstantially a maximum.

It is a further object of my invention to provide a method for heating acharge wherein the characteristics of the elements partaking in theheating operation are so related to the properties of the charge thatthe power factor of the" energy developed in the charge is substantiallya maximum.

Still another object of my invention is to provide a method of operatingan inductive-heating system according to which the charge is sodimensioned that ay maximum power factor -is obtained. A

An additional object of my invention is to provide inductive-heatingapparatus wherein the cooperating elements are so related that the firstcost of a high-frequency motor-generator set is eliminated.

` A still further object of my invention is to provide inductive-heatingapparatus wherein the continued cost arising from the losses engenderedin using a high-frequency motor generator set is avoided.

It is still another object of my invention toxincrease' the economy ofinductive heating, as applied to industrial processes.

An ancillary object of my invention is to provide inductive-heatingapparatus wherein the energy-input distribution inthe charge issubstantially uniform.

Another ancillary object of my .invention is to provideinductive-heating apparatus capable of producing a predeterminedtemperature distribution, in an element treated therein, with a minimumdegree of heat conduction.

More specifically stated, it is an object of my invention to provideinductive-heating apparatus wherein the cross section of a charge, itspermeability and its conductivity are so related to the frequency of theinducing magnetic field that a substantially maximum power factor isattained at comparatively. low standard frequencies.

According to my invention, I provide an inductive heater dimensioned incompliance with the restrictions defined by a mathematical relationexpressing the condition that the value of the vpower factor in terms cfthe constants of the apparatus and the properties of an arbitrarilyassumed charge, shall have an optimum value. In

-the following analysis, it will be shown that it is possible to use acomparatively low frequency by properly adjusting the remaining variableproperties of the heating apparatus.

Other objects of my invention will become evident from the followingdescription, taken in conjunction with the accompanying drawing, inwhich:

Figure 1 is a sectional view showing schematically an inductive heaterconstructed according to my invention;

Fig. 2 is a plan view of the apparatus shown in Fig. 1 with outer casingand insulating material removed;

Fig. 3 is a schematic View illustrating a modification of my invention;

Fig. 4 is a sectional view showing schematically the modification shownin Fig. 3;

Fig. 5 is a graph representing the solution of the power-factor problem,as applied to the apparatus shown in Figs. 1 and 2; and

Fig. 6 is a graph representing the solution of the power-factor problem,as applied to the apparatus shown in Figs. 3 and 4.

The apparatus shown in Figs. l and 2 includes a solenoid 1 comprising aplurality of turns of a flattened conductor 3. The cable is surroundedby suitable heat insulating material 4.

Adjacent to the internal surface of the solenoid 1 is a layer ofrefractory material 5 of torroidal cross section. The charge 7 isdisposed within the insulating cylinder 5. Y

Figs. 3 and 4 represent, dia'grammatically, an inductive heater capableof eiiiciently accom- `modating a charge that is rectangular in crosssection. In the treatment to be hereinafter described,l the equipmentrepresented in Figs. 3 and 4 will be regarded as having a length that islarge, in comparison with its width and depth; that is to say, I shallregard it as extending indefinitely in the direction W while its width2r and its depth L are denite.

In analyzing the problem, I shall set up and solve the Heaviside-Herzequations for the electro-magnetic iield, thus obtaining the diierentialequation which governs the flux distribution in a charge subject to amagnetic iield. In the treatment, it will be implicitly assumed that thewave length, in space, of the inducing current is great in comparisonwith the dimensions of the apparatus. I

I shall further solve the differential equation for the special case ofa cylindrical and an elongated rectangular charge, making certainobviously allowable approximations. Vlin equation defining the specialproperties of the ux distribution in the charge is thus obtained.

From the relation giving the ux distribution,

I shall obtain the components of the inducedvoltage that give rise tothe heatless component and the heat component of the power. The relationinvolving the ratio of these two values I shall then treat for optimumconditions, solving the equation, thus derived, graphically to obtain anexpression relating to properties of the vcharge and the characteristicof the inductive heater.

In the analysis, the physical properties of the elements involved arerepresented as follows:

R=internal radius of the coil in centimeters r=the radius of thecylindrical charge in centimeters :one half the width of the rectangularcharge L=the depth of the charge in centimeters W=the length of therectangular charge A=conductivity of the charge in mho 4per centimetercubed A :permeability of the charge H=strength of the magnetic' field,threading the charge, in Gilberts per centimeter =maximum flux densityin lines per square centimeter parallel to the axis of the solenoidB..=;S1e12m Where B2 is the z component of B =frequency t=tirne variableJ=inducing current I=current density in the charge E=induced voltage percentimeter of length =total ux The field equations are (1) curi H=.4iE(2) curl E=g1o therefore (3) Curl Curl -H=.4^u}( Curl E 5B (4) .41r}\510s (5) Curl cui-1 B= .mani-104 5B (6) Grad Div B-A?B= -1 .fl'rM--IO s Theend eiect in the solenoid may be safely neglected without appreciablyaecting the accuracy of the solution and the induction may be regardedIas having a direction parallel to the axis of the solenoid, i. e.,using the conventional coordinates, the components of B are given bytherefore (11) becomes (16) Ala-:.anfpiw For a cylindrical charge, themost satisfactory approach to the problem is made withY the help ofcylindrical coordinates in which terms (16) becomes Equation (20) isBessels equation of the zeroth order of which the solution is Now it isat once seen that, since is always finite, it is finite when r=u=0. Thisrestriction may be regarded as a boundary condition.

Hence it follows' that y 1,995,911 o 3 and since it is my purpose tovary :c1 as will be seen hereinafter. (25). B=AJ(") The iiux 90 out ofphase with J is given by (26) =A]0(-jmr) 21B! (27) :A 1 Lzz- Lf- JLM(41) K=Ffw The heatless component of the voltage 1s essen- (23) =Albr(mfH-J b1 (11101' tially proportional to J, while the heat comwhereinponent of the voltage is proportional to K and the constants ofproportionality do not vary A For brevity I shall write Let 6=the anglethe cosine of which is the power factor.

(3) 'SAGU xl'j b x) Hence the power factor is measured by where v X, xs(42) cot 0=7gf=7 fg? To determine A, I apply a second boundary L P Y Kx)vand the equation (30) becomes For a maximum power factor, thederivative with respect to :c of the fraction in :c and r in I equation43) is 0; that is,

m12 where (36) ci het bei" For brei/ity shall now Write` It is seen'thato comprises two components namely in phase with the inducing current Jand which may be taken as equivalent to for all practical purposes. Thiseld is in phase with the inducing current J.

Hence the total flux in phase with J is given by Q is constant if theassumption is :aaee the gap between the coil and the charge isproportional to the radius of the charge.

`bei' x ber z -f-beix bei' x* f(x)+ x' Equation (51),may besimplied to aform K (sa) wxLkiewfco-gao] .This equation may be solved graphically for:c and its solution for several values for parameter Y ,isshowninFig. 5.s

' duces to the vertical equivalent to rout/.8Min

is greater than 2.5 and has a value determined hy the gap between thecoil and the charge. In furnaces constructed according to the teachingsof the prior art, a: has avalue greater than '7.03.

- The actual value of :1: that -is chosen for any given case is notarbitrary within the limits but depends on the most convenient valuethat may be given to Q; that is, to the distance between the coil andthe charge. n

In practice, the smallest value that Q has is .05.

t is seen from the curve that a value of 5.25 for as' corresponds tothis value of Q.l The relation that dominates the dimensions of` thefurnace and the adjustment of the frequency of the current, therefore,reduces to Under ordinary circumstances, c has` a value of unity at thetemperatures at which the heater is used, while the maximum value of Ais Ai-lii'i. Hence, a more specic expression ior the Equation 54 is l'shall now consider the case wherein the charge has the cross-section ofa rectangle the length ci which extends indenitely. In practice, theerom-section oi a charge may he simply an elongated rectangl It has alsobeen found that the solution which will be obtained hereinafter may,with reasonable accuracy, be applied to a charge that has across-section in the form of an ellipse having a long major axis and ashort minor axis.

Since the cross-section of the charge is indenniteiy long, the eiect atthe ends of the charge may be neglected. Hence, ii is expressed withreference to the rectangular coordinates w, in the direction o thelength, and r, in the direction ot the width, it is seen that is afunction ci r only,

that is,

' Equation i6 holds for any geometric forni Aof charge and, when writtenin terms oi f and in, reduces'to a2 (s1) aanname-9 de e (se) g=2im where(59) m12.- .amano- I Equation 58 is a linear dierential equation noemenhaving constant coeicients, and its solution may easily be shown to becosh mr cos mrfi-j sinh nir sin mr wherein =1 for r=r'1, 2n being thewidth of the charge.

Again I! =217Vj1 d (61) b o r lo and when the indicated voperation isperformed it is found that 28,177 sinh mn cos mrl-i-j cosh mn sin mn(1+j)zn cosh mr; cosmrl--j sinh mr; sin mrl which in more simple ionnappears as cosh 2mr1-l-cos 2mn It is to be noted that the constant m, asdened byv the Equation (59),. is the m o the Equation (18) divided by f3c i i v In Equation (64) (es) x=2mr==r1ow1mpff 35 sinh x--sin x (66)F@Q -cosi: x-i-cos x sinh x-sn n (67) 'Huy-cosh x-l-cos x 40 A'me totalaux 'm phase with the inducing eurrent .i is now given by 1, zama-r) g(en a-mvve e+---/ n (69) afge/Foz) 'and 5'0 i, im S--ffa where 55 R-r.(71) Q- and is assumed toremain constant Q so F'(X)+ iv i @[1 Q31] 72)5' for) eco i Q RXE?? ee (73) 3?(10575- 1 (QW which may be written ceFcme-wwam-na} 7@ where .Y Us) Mzxoosh x-cos x sinh n-sin x The solutionof the Equation' (74;) for various 75 values of Q is shown in Fig. s. Itis seen that, in this case, the dominating inequality is (76) 2.25f1o1/1.6Mfr 9.91 a more restricted inequality being and is the valuedetermined by the prior art.

It is seen that the rectangular (or elliptic) charge yields a maximumpower factor for a width smaller than the diameter of the correspondingcylindrical charge. This property of the system is of` advantage insituations where it is desirable to use a long and narrow charge. It canbe applied with facility to apparatus wherein steel strip is normalized.

After the strip passes between a pair of rollers, it traverses anelongated induction heater where it is raised to the temperature that ithad before it came under the action of the rollers. It is then rapidlycooled. Steel treated in this manner has more desirable properties thanannealed steel.

For p=l and for a maximum value of 4-l04 for A ('15) becomes (7s)2254079515 f 9.91 for :r1- d0 cycles (T8) becomes When magnetic chargesare heated, the permeability is ordinarily of the order of 200.

For such a case, (76) becomes` i having been taken equal to 4104.

I do not wish to be restricted to the speciiic structural details orarrangement of parts herein set fortlnas various modiiications thereofmay be eiected without departing from the spirit and ratus in suchmanner that a predetermined enl ergy-input distribution for the chargeis obtained for any given situation.

The energy input per unit time for the cylindrical charge is given bythe relation Ell (81) T but by Equation 1 and, by substituting in(81),.it isseen that the absolute value of the energy developed is givenby 83) m58;2 berx+bei"x .813)44 berxx-i-beixl For a rectangular charge,the absolute value oif the energy input is given by z mz cosh x-cos x('84) W .41:42AM cosh x1+cos x1 These relations are of particularinterest in certain elds of industry e. g., in rolling mills where it isnecessary to relieat an ingot after it has been removed from the moldand prior the rolling operation.

When the ingot is poured, the entire mass of metal may be regarded ashaving a uniform temperature. As a result of the thermal capacity of thewalls of the mold, the ingot, when removed from the mold, is not ofuniform temperature throughout but has a maximum temperature in someinterior region and has a minimum temperature on its bounding surface.ll

In reheating the ingot before rolling, it is desirable that it bebrought back to substantiauy a uniform temperature throughout, the valueof will be approximately the same ats-.the temperature at its hottestpart when it was removed from the mold.

In general, it is possible to determine the theoreticaltemperature-distribution characteristic of any ingot of givendimensions, and to sc adjust the properties of the inductive retreatingapparatus in which the ingot is treated that the power input in eachindividual region of the ingot is substantially proportional to thetemperature through which the metal in these regions is to be heated.For example, in a cylindrical ingot, the

temperature distribution varies parabolicallyV from the center to theperiphery. It is obvious that the constants of the heating apparatus maybe so selected that W, in Equation (83), varies substantially as aparabola similar to the inverted temperature-distribution curve.

As a result of such specific arrangement of the apparatw, the heatingenergy is liberated in individual regions in proportion as it is needed,and it is not necessary to allow time for heat flow from an abnormallyheated region to a cooler region. I have found that this process reducesthe reheating time from several hours to approximately 10 minutes.

I desire, that only such limitations shall be imposed upon my inventionas are indicated in the appended claims.

I claim as my invention:

1. Inductive electrical heating apparatus comprising a coil to bemagnetically coupled to a. cy-

lindrical charge, a substantial air gap intervening between said coiland charge and an alternating source of current for energizing saidcoil, the characteristics of said coil and said source being so relatedto each other and to the properties of said charge that theysubstantially obey the relation Y where Y 'l b l wherein ber x be' x-beix er x F(X)=X ;T; Vxf Y A 2:11-10-1/.8Mfr

berm X+beil2 x rl being the radial distance from the axis of said (X)=mmass o f a point at which W is the energy input b b HJ b A being theconductivity of sa1d mass f(x)=x-fzxel.x a being the permeability ofsaid mass Y s ber x-He x f being the frequency of said magnetic eldQ=R2zz3 x,= 1o-alinea, r1 being the radius of said mass 1 tsm p1=theamplitude of the aux density at the T ithseggifnge Charge periphery ofthe mass and n Y X being its'conductivity m=1r1/ 10.94131 R being theradius of the inducing coill and being the frequency of the current. i

wherein sinh x-I-sn x F(X) cosh x-icos r' l sinh x-sin x l(x) coshx-l-cos x SEM-9.5.2. sinh x-sin z R-r Q= 1.

l x= 211'1041/.4pir

2r being the width of the charge A being its conductivity p. being itspermeability f being the frequency of the curren 2R being the width ofthe heating coil.

A3. The method 'of heating a furnace charge, which is in the form of acircular cylinder, from an initial condition in which it has atransverse temperature distribution function which is substantlally aparabola with an'- axis coinciding with the central axis of thecylinder, which consistsv in generating heat Within the cylindricalmass,

the rate of heat generation having a substantially parabolicdistribution relative to said central axis.

4. The method o heating a furnace charge, which is in the form of acircular cylinder, from an initial condition in which it has atransverse temperature distribution function whichris substantially aparabola with an axis coinciding with the central axis of the cylinder,which consists in generating heat within the cylindrical mass, the

' rate of heat generation having a distribution which is a parabolasubstantially similar to the fast-mentioned parabola and is coaxialtherewith.

5. The method of heating a furnace charge,V

which is in. the form of a circular cylinder and y which has 'cooledfrom a substantially uniform elevated temperature condition by heatoutow from its side walls, which consists in generating heat byelectromagnetic induction .within said cylindrical mass by means of an'alternating magnetic eld such that the rate W of heat generation ulllsthe equation v f z .,rrlll2 bei'.I2 x-l-be2 x .812)412 berg Iliff-bei?X1 wherein 6. The method of heating a rectangular conducting Vmass,having the form of a rectangular Y parallelopiped, which has cooled froma substantially uniform elevated temperature condition by heat outflowthrough two opposite side Walls,

which consists in generating heat within said mass by electromagnetic4induction through the agency o an alternating magnetic field such thatthe rate W of heat generation fulils the equation mzl2 cosh x-cos zAa-ZAM cosh xl-i-cos :x1

x=2fr1o1lniufr 'r being the distance in said mass from the center lineparallel to its longest side at which W is the energy input Fano-a!.gaten 2n being the width of said mass and '71. The method of heating afurnace charge, which is in the form of a circular cylinder and whichhas cooled from a substantially uniform elevated temperature conditionby heat outilow from its side walls, which consists in generating heatby electromagnetic induction within said cylindrical mass by means of analternating niagnetic field such that the rate W of heat generationfullls the equation wherein `1'1 being the radius of said Ymassperiphery of the mass and m=1r1lr41jlli the constants of the heatingapparatus being so selected that lin the above equation variessubstantially as a parabola similar to the invertedtemperature-distribution curve. Y 8. The methodl of heating arectangular con ducting mass, having the form of a rectangularparallelopiped, which has cooled from a substantially uniform elevatedtemperature condition by heat out-ow through two opposite side walls,

which consists in seneratins heat within wld ter line parallel to itslongest side at which W is mass by electro-magnetic induction throughthe the energy input agency of an alternating magnetic held such thatthe rate W of heat generation tuliills the equation x: 2'! TH/md 13.41%# coahl-i-coo xl t m=r10m l wherein the constants of the heatingapparatus being so I selected that W in the above equation varies sub-10 x=2,10-1/ 4' `T, stantially -as parabola similar to the inverted 10 Atemperature-distribution curve. r being the distance in said mass fromthe cen- THOMAS E. LONG,-

`2nheimrthe widthofsaidmassand 5

